Gravitino production after inflation 2156.3 Gravitino production after inflation
During the last couple of years there has been a growing interest in understanding
gravitino production in the early universe [3, 14]. The general consensus is that
gravitinos can be produced during pre-heating after inflation due to a combined
effect of interactions with an oscillating inflaton field and because the helicity
± 1 /2 gravitino have equations of motion which break conformal invariance. In
general the probability of gravitino production isnotsuppressed by the small
gravitational coupling. This may lead to a copious production of gravitinos
after inflation. The efficiency of the new non-thermal mechanism of gravitino
production is very sensitive to the choice of the underlying theory. This may put
strong constraints on certain classes of inflationary models.
A formal reason why the effect may be strong even at MP →∞is
the following: in Minkowski space the constraint which the massive gravitino
satisfies has the form
γμψμ= 0. (6.7)In an expanding universe, the analogue of equation (6.7) looks as follows:
γ^0 ψ 0 −Aˆγiψi= 0 (6.8)where, in the limitMP→∞,
Aˆ=p
ρ+γ 02 W ̇
ρ, |Aˆ|^2 = 1. (6.9)
MatrixAˆrotates twice during each oscillation of the fieldφ. The non-adiabaticity
of the gravitino fieldψ 0 (related to helicity± 1 /2 is determined not by the mass
of the gravitino but by the mass of the chiral fermionμ=Wφφ. This equation
was obtained in the framework of a simple model of the supergravity theory
interacting with one chiral multiplet. The gauge-fixing of the spontaneously
broken supersymmetry was relatively easy, the only one available in the model
chiral fermion, a goldstino field, was chosen to vanish and the massive gravitino
was described by helicity± 3 /2 as well as helicity± 1 /2 states.
A physical reason for gravitino production is a gravitino–goldstino
equivalence theorem which, however, had to be properly understood in the
cosmological context.
One of the major problems with studies of gravitino production after inflation
was to consider the theories with few chiral multiplets. It become clear that one
cannot simply apply the well-known super-Higgs mechanism of supergravity in
the flat background to the situation in which we have a curved metric of the early
universe.